PHYSICAL REVIEW
LETTERS
6 MAY 1985
VOLUME 54
NUMBER 18
Neutron Microscope
P. Herrmann, ( a ) K.-A. Steinhauser, R. Gahler, and A. Steyerl
Fakulfatfur Physik, Technische Universitat Miinchen, D-8046 Garching, Germany
and
W. Mampe
Institut Laue-Langevin, F-38042 Grenoble, France
(Received 18 February 1985)
We report successful operation of a neutron microscope using ultracold neutrons at the high-flux
reactor at Grenoble. A sharp, achromatic image of an object slit was obtained at a magnification of
50. The measured resolution of 0.1 mm was limited mainly by the available beam intensity, not by
aberrations.
PACS numbers: 07.80. + x, 29.25.Fb, 41.80.-y
Neutrons interact with matter quite differently than
photons (light or x rays) or electrons. Therefore they
"sense" a different contrast.
Thermal-neutron
scattering in combination with controlled protondeuteron exchange is nowadays established as a unique
and extremely powerful method for probing the hydrogen distribution in matter. The availability of ultracold
neutrons 1 " 3 (UCN) has opened the possibility of exploiting the "neutron contrast" also in a neutron microscope. This appears feasible since ultracold neutrons are totally reflected from suitable mirror materials even at large angles of incidence, and thus anastigmatic imaging systems can be developed.
However, in contrast with light, UCN beams are
curved by gravity, and the wavelength dependence of
curvature gives rise to chromatic aberrations of mirror
systems. The properties of a concave mirror as a system for UCN imaging were first described by Frank in
1972.4 For realistic applications the gravitationally induced chromatic aberrations must be corrected.
In the first neutron imaging system meeting this criterion 5,6 correction of the longitudinal chromatic aberration (in focal length) to first order was achieved by
use of a "zone mirror" consisting of a totally reflecting, blazed zone grating deposited on a concave spherical mirror with vertical optical axis. Compensation of
gravity by a homogeneous magnetic field gradient was
proposed by Skachkova and Frank. 7
The present paper reports experimental results obtained with a prototype of an achromatic two-mirror
neutron microscope with a magnification of 50. As
previously described 8,9 it is designed so as to correct
both the longitudinal and the transverse chromatic
aberration (wavelength dependence of magnification)
to first order. Successful operation of a different,
four-mirror system with magnifications 1.375 and
0.725, designed for chromatic correction at high
enough velocities, was recently reported. 10
Fermat's principle of stationary phase implies 5 ' 9 that
in the presence of a constant force field acting purely
in the vertical z direction the imaging equation for a
curved mirror with optical axis in the z direction
reads, 4,5 for paraxial rays,
2_
R
1
di
1
1
I
h+
i
h\
(1)
where R is the radius of mirror curvature, v is the
neutron velocity at mirror height, and t\ ( / = 1,2) are
the neutron flight times between mirror center and object or image points. Equation (1) is identical to the
imaging equation for straight rays except for a replacement of the acutal flight paths, dh by those for straight
rays, d*, intersecting the mirror surface at the same
angles as the curved particle rays. The magnification is
given by /JL = t*Jt\. All the relevant quantities, g (grav-
© 1985 The American Physical Society
1969
V O L U M E 54,
NUMBER
18
PHYSICAL REVIEW L E T T E R S
itational constant), v, R, dh and th can assume positive or negative values, depending on the actual
geometrical configuration.
For a concave mirror the object distance dx = R/2
(at the light-optical focus above the mirror) is distinguished in the sense that the image formed at
d2= R/2 = di by the rays after passing the maximum
height of their flight parabola, H = v2/2g, is free of
longitudinal chromatic aberration to all orders. However, for this case the magnification /x — SH/R ~ v2
(for H » R/2) is strongly chromatic.
A possibility of compensating both first-order
chromatic aberrations arises for a system of two mirrors arranged one above the other on their common
optical axis. We consider specific configurations subject to the conditions dd^/dv^O
and 8M/9v = 0,
where the primes refer to the secondary mirror system
and M = ixfx' is the overall magnification. After extensive algebra we find the following relations for twomirror achromatic systems:
2/ai = 2T? + 7 ? f 1 - l
(2)
and
^
2
,
=
2
V\(vi~v)
T7-2T7!+1
a[ 17(T?I + 1) — 5T7J + 3 '
where we have used the dimensionless quantities
i = vlv\
ff-Vy/V, a^-gt^/v',
and T7(i)=(l
+ f ( i ) ) / ( l —£(i>). The connection between the two
mirror subsystems via the common intermediary
image/object is expressed by the relation a2
= l-£-ai.
We may regard the total magnification, M = /x/x',
and 171 (a measure of object position) as independent
parameters determining the possible geometries of the
optical system. For given M a n d r) \ two values for 77
may be found from the quadratic equation M=M(iq,
T?!) . Only a small subset of solutions satisfies the following criteria: (a) 17 must be real valued and such
that both object and final image will be real and the
mirrors are hit by real, not virtual, rays, (b) The mirrors, object or image scanning device, supports, etc.,
should not block a substantial fraction of the possible
flight paths, (c) It is preferable to arrange the object at
a short distance above the primary mirror, and below
the secondary one, in order to make optimum use of
the source UCN spectrum which in all practical cases is
depleted at the lowest energies.
A common feature of all systems meeting these criteria is the following: The neutrons pass the highest
point of their flight parabola on their way between the
two mirrors. Only for such configurations can the
first-order chromatic aberrations of one mirror be
1970
6
MAY
1985
compensated by those of the other mirror. For this
class of instruments it was found impossible to correct
chromatic aberrations of higher order since terms like
b2d{/bv2 or d2M/dv2 remain finite. Large magnification, \M\ » 1, can be achieved either if \/m\ » 1
(hence r? — 7^) or if |/x'| » 1, but only the former
case corresponds to a system with a real object. Furthermore, M—• +00 (the + sign indicating that the intermediary image is real) may be excluded on account
of postulate (c).
Finally, we may choose v (or v') and thus the common scale factors: v' for velocities, v'/g for flight
times, and v'2/ gfor lengths. For systems utilizing total
reflection from the mirrors, \v\ and \v'\ must lie
below the critical value vh (For instance, for 58Ni the
lower of the two values for the two spin states is
v/ = 7.5 m/s.)
The following design parameters were chosen for
the present experiment: M= — 51.94, r/j = —0.14294,
and v = 5.73 m/s. The associated geometry is as follows (see Fig. 1): ^ = 293.1 mm (object above primary mirror); i? = 585.2 mm (concave) and R'
= —1209.8 mm (convex); mirror separation, 897.5
mm (second above first); intermediary (virtual) image
distance below, and final image distance above, the
second mirror, d{ = — 415.1 mm and d2 =662.7 mm;
partial magnifications, /x = 20.10 and/x' = —2.58; velocities, e.g., |v 1 | = 5.204 m/s (at the object) and | i / |
= 3.903 m/s (at second mirror).
A detailed analysis of higher-order aberrations was
Image Mirror
^ ^
Detector
— Secondary
Mirror
— Movable
Object
Slit
— Parabolic Mirror
FIG. 1. Scheme of the two-mirror neutron microscope
setup. Neutron trajectories are shown for two different
velocities. The neutrons pass the highest point of their
flight parabolas between the imaging mirrors. This is a
necessary condition for compensation of both chromatic
aberrations (in focal length and in magnification) to first order. The instrument is designed for a wide entrance aperture (1:1.5) and for magnification ~ 50.
VOLUME54, NUMBER
18
PHYSICAL REVIEW
performed by ray tracing. The differential aberrations
(like coma) are identified with specific terms in a Taylor series for the total aberration A.
A{rx><}>\^\^\)
denotes the distance within the image plane by which a
specific ray misses the nominal image point if it leaves
the object plane at distance r\ from the axis, at off-axis
angles <f>\ (in the sagittal plane) and tyi (in the meridional plane), and at a velocity vi + w\, where vx is the
design value. The chromatic aberrations
d2A/brdw\0
= dM/dv
and
d2A/dcf>dw\0-ddi/dv
were corrected for the present system. All the
nonzero expansion coefficients up to fifth order were
calculated by numerical differentiation, and terms of
higher order were shown to be of less importance by
comparison with the total aberration, even if wide
apertures are admitted. This analysis provided the
basis for the choice of mirror diameters and mirror
shapes. Favorable results were obtained for a parabolic shape of the primary, strongly magnifying mirror.
We chose a diameter of 20 cm, i.e., an entrance aperture of 1:1.5. The geometrical aberrations (mainly
coma, b^A/br 9<£2, and spherical aberration, d3A/d<f>3)
then lie within tolerable limits of < 1 mm. The smaller secondary mirror of 5 cm in diameter can be spherical without loss in imaging quality. For the full velocity band 5.5 < v/(l m/s) < 6.7 (as determined by the
image mirror height and the overall height of the apparatus) the uncompensated chromatic aberrations of
higher order are dominant (several millimeters).
The image field width is limited by the requirement
that the scanning device, an ''image mirror" reflecting
the neutrons into a detector, should constitute a negligible obstacle for the neutrons on their descent to the
secondary mirror. An image field width of 17x17
mm 2 was chosen, corresponding to an object of
0.35x0.35 mm 2 . In principle, the image could be
resolved into two-dimensional elements of a size limited by the aberrations by use of a facet-type mirror reflecting neutrons from different image zones into different detectors. For the present prototype of a microscope we chose a single fixed-image mirror of 17 x 17
mm 2 , inclined 15° to the horizontal plane, and spherically concave. This ensures collection of nearly all
neutrons arriving at the image mirror in an inclined,
convergent, guide tube of entrance section 2.5x4.5
cm2 which conducts them to the detector (BF3 with reduced 10B content). The detector is placed 0.7 m
below the image plane, and thus the slowest neutrons
gain enough kinetic energy for passing through the
detector window (0.1-mm Al with open section 2.5x2
cm 2 ; for Al, v, = 3.2 m/s).
We used the guide-tube facility PN5 11 at the high-
LETTERS
6 MAY 1985
flux reactor at Grenoble, supplying a current density
of ==100 UCN/cm 2 -s. Since the microscope utilizes a
very wide beam divergence, we installed a convergent
guide section in front of a slit serving as the object.
The primary beam profile can be scanned with use of a
monitor detector mirror inserted below the object slit.
The imaging mirrors were fabricated from Zerodur and
coated with nickel (the primary mirror with 58 Ni).
Computer simulations for maladjusted configurations showed that very precise adjustment, especially
of the primary mirror and of the object position, was a
crucial requirement. Sufficient precisions of — 10 ~ 4
rad in mirror horizontality and of —0.1 mm in object
distance were achieved with use of light-optical
methods. The system was pumped to < 10" 4 mbar.
The microscope was designed for object scanning.
The scan perpendicular to the object slit was performed by use of a stepping motor controlled by a microcomputer (MACAMAC) which served also for data
collection and reduction.
For a test of the specific one-mirror system
described above the secondary, small mirror was removed and an image mirror, inclined at 45° and intercepting 1.5x1.5 cm 2 of the beam, was installed at a
short distance of 80 mm above the object slit. The object slit was placed just above the optical focus of the
primary mirror to compensate for the slight deviation
from the ideal geometry where object and image
should coincide in the light-optical focus. The detector and a short feeding guide tube were placed so as to
collect the neutrons reflected from the image mirror.
The magnification is 25 at v = 6.2 m/s but varies as
~~ v2. Figure 2(a) shows the data obtained in a scan of
the 1.06-mm-wide object slit. The edges are blurred as
a result of the wide velocity range accepted. The measured curve agrees well, even in absolute height, with
a computer simulation (dashed curve) where the broad
incident neutron spectrum was taken into account and
the monitor data for the beam profile were used.
Figure 2 (b) shows the result of a similar scan for the
two-mirror microscope setup of Fig. 1. The data
points are consistent with an edge width of —0.3 mm,
as expected for a magnification of 52 and the image
mirror width of 17 mm (see the solid curve).
We have reported successful operation of a novel
neutron microscope characterized by a magnification
of =^ 50 and full achromatism to first order. The resolution of —0.1 mm observed was limited by coursegrained image detection, and this, in turn, was dictated
by the modest UCN source strength. Future UCN
sources are expected to be ~ 102 times stronger (e.g.,
see Ageron and Mampe 12 ). The present aberration
limit to the resolution (in two dimensions) is ^ 0.02
mm, but can be reduced, say, to several micrometers,
by coarse incident-beam monochromatization. This
would require higher magnifications which are possible
1971
V O L U M E 54,
N U M B E R 18
P H Y S I C A L REVIEW L E T T E R S
6
MAY
1985
flight parabola between the mirrors is of order 1 c m / s .
This is close to the range ^ 1 0 ~ 5 m / s for the
" s n a i l ' s - p a c e " neutrons introduced by Shull. 1 3
This research was supported by the G e r m a n Bundesministerium fur Forschung und T e c h n o l o g i c T h e
invaluable technical help by H. Nagel and F. X.
Schreiber was essential for the success of this work.
We are highly indebted to the Institut Laue-Langevin
for generous support, and for active help we thank P.
Ageron,
O. Scharpf,
A. Beynet,
F.
Epaud,
B. R. Heckel, P. Miranda, Mrs. G. Creighton, and
Mrs. S. Neumair. Useful discussions with W. Glaser
are acknowledged.
SLI T
P O S ! TIO N
( mm )
FIG. 2. Data for scans of a 1.06-mm-wide object slit (a)
for the specific one-mirror system where (ideally) object and
image coincide at the light-optical focus, for any arbitrary
neutron velocity; and (b) for the two-mirror microscope setup of Fig. 1. In (a) the magnification is strongly chromatic,
and this leads to the observed edge blurring for the wide
UCN spectrum used. The trapezoidal image in (b) implies a
resolution of —0.1 mm. It was limited by coarse-grained
image detection rather than aberrations. The measured data
are consistent with calculations (dashed and solid curves).
Measurement (a) was performed at a reduced primary intensity (factor of 6).
for two-mirror schemes of the present topology. T h e
problems of chromatism and intensity can be relaxed
by choosing higher speeds around 12 m / s and multilayer mirrors, as proposed previously. 8
W e point out an interesting by-product of the
present research. At the classical reversal point for
vertical particle motion in the gravitational field the
velocity vanishes. In the present experiment the
m i n i m u m neutron velocity at the highest point of their
1972
(^Present address: Max-Planck-Institut fur Quantenoptik, D-8046 Garching, Germany.
1
F. L. Shapiro, in Nuclear Structure Study with Neutrons,
edited by J. Ero and J. Szusc (Plenum, New York, 1975), p.
259.
2
A. Steyerl, in Neutron Physics, edited by G Hohler,
Springer Tracts in Modern Physics, Vol. 80 (SpringerVerlag, Berlin, 1977), p. 57.
3
R. Golub and J. M. Pendlebury, Rep. Prog. Phys. 42, 349
(1979).
4
I. M. Frank, Priroda 9, 24 (1972).
5
A. Steyerl and G. Schiitz, Appl. Phys. 17, 45 (1978).
6
G Schiitz, A. Steyerl, and W. Mampe, Phys. Rev. Lett.
44, 1400 (1980).
7
0 . S. Skachkova and A. I. Frank, Pis'ma Zh. Eks. Teor.
Fiz. 33, 274 (1981) [JETP Lett. 33, 203 (1981)].
8
P. Herrmann, "Ein Neutronenmikroskop fur ultrakalte
Neutronen: Entwicklung und erste Messungen", Dipl.
thesis, Technische Universitat Miinchen, 1982 (unpublished).
9A. Steyerl, J. Phys. (Paris), Colloq. 45, C3-255 (1984).
10
S. S. Arzumanov, S. V. Masalovich, A. N. Strepetov, and
A. I. Frank, Pis'ma Zh. Eks. Teor. Fiz. 39, 486 (1984)
[JETP Lett. 49, 590 (1984)].
n
P . Ageron, M. Hetzelt, W. Mampe, J. M. Pendlebury,
J. M. Robson, and K. Smith, in Proceedings of the International Symposium on Neutron Inelastic Scattering, Vienna, 1977
(International Atomic Energy Agency, Vienna, 1978),
Vol. 1, p. 53.
12
P. Ageron and W. Mampe, J. Phys. (Paris), Colloq. 45,
C3-279 (1984).
13
C. G. Shull, in The Neutron and Its Applications—1982,
edited by P. Schofield, IOP Conference Proceedings No. 64
(Institute of Physics, Bristol, London, 1983), p. 157.